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SUMMARY:On the radius of Gaussian free field excursion clusters - Franco S
 evero (Geneva and IHES)
DTSTART:20210504T130000Z
DTEND:20210504T140000Z
UID:TALK160135@talks.cam.ac.uk
CONTACT:Perla Sousi
DESCRIPTION:We consider the Gaussian Free Field (GFF) on $\\mathbb{Z}^d$\,
  for $d\\geq 3$\, and its excursions above a given real height $h$. As $h$
  varies\, this defines a natural percolation model with slow decay of corr
 elations and a critical parameter $h_*$. Sharpness of phase transition has
  been recently established for this model. This result directly implies\, 
 through classical renormalization techniques\, that the radius distributio
 n of a finite excursion cluster decays stretched exponentially fast for an
 y $h\\neq h_*$. In this talk we shall discuss sharp bounds on the probabil
 ity that a cluster has radius larger than $N$. For $d\\geq 4$\, this proba
 bility decays exponentially in $N$\, similarly to Bernoulli percolation\; 
 while for $d=3$ it decays as $\\exp(-\\frac{\\pi}{6}(h-h_*)^2\\frac{N}{\\l
 og N})$ to principal exponential order. We will explain how the so-called 
 "entropic repulsion phenomenon" allows us to prove such precise estimates 
 for $d=3$. This is a joint work with Subhajit Goswami and Piere-François 
 Rodriguez.
LOCATION:Zoom
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